It looks like you're working with equations where the unknown variable \( x \) is raised to certain powers. Let's solve them step by step.

### a. \( x^3 = 1.57 \)
To solve for \( x \), we need to take the cube root of both sides:

\[
x = \sqrt[3]{1.57}
\]

Using a calculator, we get:

\[
x \approx 1.165
\]

### b. \( x^5 = 1620 \)
To solve for \( x \), we need to take the fifth root of both sides:

\[
x = \sqrt[5]{1620}
\]

Using a calculator, we get:

\[
x \approx 4.273
\]

So the solutions are:
- \( x \approx 1.165 \) for \( x^3 = 1.57 \)
- \( x \approx 4.273 \) for \( x^5 = 1620 \)

Would you like further explanation on these steps?

Here are 5 related questions you might find helpful:
1. How do you solve higher powers of \( x \), like \( x^7 = a \)?
2. What is the difference between even and odd roots when solving for \( x \)?
3. How can we approximate roots without a calculator?
4. What is the geometric interpretation of cube roots and fifth roots?
5. Can cube roots and fifth roots have negative values?

**Tip**: For powers greater than 2, you can use calculators that support roots (cube, fifth, etc.) or logarithms to solve for \( x \) efficiently.

This tutorial walks you through solving equations like x^3 = 1.57 and x^5 = 1620 by applying cube and fifth roots. Learn the key algebraic steps and formulas to solve for x in these types of exponentiation problems. Ideal for high school students (Grades 9-12).

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